Just a few comments to avoid misunderstandings
#1. I don't think there is such limitation, as far I know you can have both running on the same machine (EP/NWDI)
Correct, but the NWDI should be standalone. It is a system, which is available accross all landscapes (development, quality, ..., production). A enterprise portal is just for a specific stage like quality. If you mix up the applications, you will not be able to isolate the individual landscapes anymore. Also you do not want to take a risk to corruped your NWDI, because if this one does crash as of development work at other applications, you will loose your source codes and face a painful process to recover those.
#2. Biller Direct does not need to run under anything 'SAP' branded, you can extract and run it locally in a Tomcat if you want, -- also, there is no real need for NWDS as far I'm aware.
Not correct, Biller Direct is tightly integrated to SAP's Netweaver environment. There is not chance you get it working within Tomcat, unless you rewrite the whole front-end. It already starts with the XCM (wich can be solved), then the SAP User Management, etc. Biller Direct is depending on those services / interfaces.
#3. Since you don't need a bloated AS like NetWeaver to develop, you can just use a Tomcat or Jetty Container pointing directly to the root folder - you would have 'instant' access to modifications, (change in eclipse, save and hit f5 in the browser)
I think the previous paragraph did already provide the answer: not working.
The whitepaper you provided is good, but making this working takes quite some time. It is also written for SAP E-commerce and yes, Biller Direct is partially re-using some elements of E-Commerce (ISA) like XCM. However, the main issue of Biller Direct is .... the developer had no experience how SAP ISA works and hence did just partially use some elements and wrote most of the logic himself. Also the whole login process is not the same as ISA, it completely relys on the NetWeaver - SAP ISA still had all processes within it's own application. You also will be forced to clean up any JSP page from some NetWeaver specific implementations like the cross site scripting feature, which was implemented to quickly.
Somehow you will get it working, but that will take serveral months and a lots of expertise to get the site effects under control. ISA is compared to Biller Direct a "Kindergarten", not because of functionality, but becaue of the architecture and the way of how the coding was done.